To solve this problem, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where A is the amount of money at the end of the investment period, P is the principal (initial investment), r is the interest rate (expressed as a decimal), n is the number of times the interest is compounded per year, and t is the number of years of the investment period.
For Brandon's account:
P = $9,200
r = 3.25% = 0.0325
n = 4 (compounded quarterly)
t = 19 years
A = 9200(1 + 0.0325/4)^(4*19) = $17,631.51
For Lamonte's account:
P = $9,200
r = 2.875% = 0.02875
n = 12 (compounded monthly)
t = 19 years
A = 9200(1 + 0.02875/12)^(12*19) = $16,031.63
The difference in the amount of money between Brandon's and Lamonte's accounts after 19 years is:
$17,631.51 - $16,031.63 = $1,599.88
Therefore, Brandon would have approximately $1,599 more in his account than Lamonte after 19 years, to the nearest dollar.